Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20295583 | C2 | semidirect |
| 3. #20295435 | C2 | semidirect |
| 4. #20295420 | C2 | semidirect |
| 5. #20295395 | C2 | semidirect |
| 6. #20295386 | C2 | semidirect |
| 7. #20295284 | C2 | semidirect |
| 9. C4×Dic436 | C2 | semidirect |
| 10. C4×#13182018 | C2 | semidirect |
| 11. C4×M16×C109 | C2 | semidirect |
| 130. C109 | #3172 | semidirect |
| 141. C4×M16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295583 | 2 |
| #20295560 | 2 |
| #20295435 | 2 |
| #20295420 | 2 |
| #20295395 | 2 |
| #20295386 | 2 |
| #20295284 | 2 |
| #20295272 | 2 |
| C4×Dic436 | 2 |
| C4×#13182018 | 2 |
| C4×M16×C109 | 2 |
| #3172 | 109 |